How to find a rational number between 3 and 4?

To find a rational number between two numbers, we can calculate the average of the numbers. The average obtained between the numbers is the rational number which lies between those numbers. We have to calculate a rational number between 3 and 4. The average of 3 and 4 is 3.5, which is a rational number that lies between 3 and 4. There are many Rational Numbers between 3 and 4 such are, 3.1, 3.2, 3.3, …, 3.8, 3.9, and so on. Thus, there are infinite numbers between 3 and 4.

In this article, we are going to learn what is rational number and different approaches to finding a rational number between two given rational numbers.

A rational number between 3 and 4 is 3.5

Before proceeding with how to find rational numbers one must know about rational numbers in brief.

Note: There are infinite rational numbers between any two rational numbers.

Numbers which can be expressed as fractions or ratios of two integers are called rational numbers. A rational number is a sort of real number that has the form p/q where q≠0 in mathematics. We may also classify any fraction as a rational number if the denominator and numerator are both integers and the denominator is not equal to zero. When a rational number is split, the result is a decimal number, which can be either a terminating or a recurring decimal.

Rational Number can be expressed as p/q, where q ≠ 0

For example, 11/13 is a rational number.

Rational numbers between 3 and 4 are 31/10, 32/10, 33/10, 34/10, 35/10, 36/10, 37/10, 38/10, 39/10. 

Apart from these numbers, there are infinite rational numbers between 3 and 4.

To find out a set of rational numbers between any two numbers suppose 3 and 5 follow various approaches added below:

Approcach 1:

Express 3 and 4 as rational numbers as

⇒3 = 3 × 10/10 = 30/40

⇒4 = 4 × 10/10 = 40/10

Now one can easily find the rational number between 30/10 and 40/10.

Hence, the rational numbers between 3 and 4 (30/10, and 40/10) are 31/10, 32/10, 33/10, 34/10, 35/10, 36/10, 37/10, 38/10, 39/10.

Approach 2:

Rational number between any two number can be easily found using the steps:

Suppose we are given two numbers 3 and 4

Find the middle number between them (say a)

a = (3 + 4)/2 = 7/2 = 3.5

Now we will find the middle term of 3 and 3.5(say b) and 3.5 and 4 (say c)

b = (3 + 3.5)/2 = 3.25

c = (3.5 + 4)/2 = 3.75

Simillarly infinite number can be found between 3 and 4 using this methods,

Question 1: What is the rational number between 7 and 9?

Solution:

Here, the given terms are 7 and 9, so the mean is:

m = (7 + 9) / 2 = 16/2 = 8

Question 2: What is the rational number between 1 and 4?

Solution:

Here, the given terms are 1 and 4, so the mean is:

m = (1 + 4)/2 = 5/2 = 2.5